LMFDB - Embedded newform 966.4.a.o.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 560x^{3} + 2247x^{2} + 58113x - 197784 $ x^5 - x^4 - 560x^3 + 2247x^2 + 58113*x - 197784
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$14.8741$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.8741 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.8741 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -31.7483 q^{10} -10.2717 q^{11} +12.0000 q^{12} -33.3338 q^{13} -14.0000 q^{14} +47.6224 q^{15} +16.0000 q^{16} +50.9562 q^{17} -18.0000 q^{18} -37.2079 q^{19} +63.4966 q^{20} +21.0000 q^{21} +20.5434 q^{22} -23.0000 q^{23} -24.0000 q^{24} +126.988 q^{25} +66.6676 q^{26} +27.0000 q^{27} +28.0000 q^{28} -46.6386 q^{29} -95.2448 q^{30} +53.8689 q^{31} -32.0000 q^{32} -30.8150 q^{33} -101.912 q^{34} +111.119 q^{35} +36.0000 q^{36} +299.874 q^{37} +74.4158 q^{38} -100.001 q^{39} -126.993 q^{40} +496.665 q^{41} -42.0000 q^{42} +286.973 q^{43} -41.0867 q^{44} +142.867 q^{45} +46.0000 q^{46} +441.691 q^{47} +48.0000 q^{48} +49.0000 q^{49} -253.977 q^{50} +152.869 q^{51} -133.335 q^{52} +404.159 q^{53} -54.0000 q^{54} -163.054 q^{55} -56.0000 q^{56} -111.624 q^{57} +93.2771 q^{58} -3.89721 q^{59} +190.490 q^{60} -758.345 q^{61} -107.738 q^{62} +63.0000 q^{63} +64.0000 q^{64} -529.145 q^{65} +61.6301 q^{66} -461.880 q^{67} +203.825 q^{68} -69.0000 q^{69} -222.238 q^{70} -814.198 q^{71} -72.0000 q^{72} +1176.38 q^{73} -599.747 q^{74} +380.965 q^{75} -148.832 q^{76} -71.9018 q^{77} +200.003 q^{78} +949.684 q^{79} +253.986 q^{80} +81.0000 q^{81} -993.329 q^{82} -141.363 q^{83} +84.0000 q^{84} +808.886 q^{85} -573.946 q^{86} -139.916 q^{87} +82.1734 q^{88} -412.219 q^{89} -285.734 q^{90} -233.336 q^{91} -92.0000 q^{92} +161.607 q^{93} -883.382 q^{94} -590.644 q^{95} -96.0000 q^{96} -573.858 q^{97} -98.0000 q^{98} -92.4451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} - 12 q^{10} - 50 q^{11} + 60 q^{12} + 66 q^{13} - 70 q^{14} + 18 q^{15} + 80 q^{16} - 198 q^{17} - 90 q^{18} + 120 q^{19} + 24 q^{20} + 105 q^{21} + 100 q^{22} - 115 q^{23} - 120 q^{24} + 503 q^{25} - 132 q^{26} + 135 q^{27} + 140 q^{28} + 301 q^{29} - 36 q^{30} + 314 q^{31} - 160 q^{32} - 150 q^{33} + 396 q^{34} + 42 q^{35} + 180 q^{36} + 269 q^{37} - 240 q^{38} + 198 q^{39} - 48 q^{40} + 479 q^{41} - 210 q^{42} - 290 q^{43} - 200 q^{44} + 54 q^{45} + 230 q^{46} + 69 q^{47} + 240 q^{48} + 245 q^{49} - 1006 q^{50} - 594 q^{51} + 264 q^{52} + 339 q^{53} - 270 q^{54} + 957 q^{55} - 280 q^{56} + 360 q^{57} - 602 q^{58} + 2065 q^{59} + 72 q^{60} + 531 q^{61} - 628 q^{62} + 315 q^{63} + 320 q^{64} + 1227 q^{65} + 300 q^{66} + 855 q^{67} - 792 q^{68} - 345 q^{69} - 84 q^{70} - 863 q^{71} - 360 q^{72} + 618 q^{73} - 538 q^{74} + 1509 q^{75} + 480 q^{76} - 350 q^{77} - 396 q^{78} + 254 q^{79} + 96 q^{80} + 405 q^{81} - 958 q^{82} - 1700 q^{83} + 420 q^{84} + 1977 q^{85} + 580 q^{86} + 903 q^{87} + 400 q^{88} - 275 q^{89} - 108 q^{90} + 462 q^{91} - 460 q^{92} + 942 q^{93} - 138 q^{94} + 171 q^{95} - 480 q^{96} - 979 q^{97} - 490 q^{98} - 450 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 - 12 * q^10 - 50 * q^11 + 60 * q^12 + 66 * q^13 - 70 * q^14 + 18 * q^15 + 80 * q^16 - 198 * q^17 - 90 * q^18 + 120 * q^19 + 24 * q^20 + 105 * q^21 + 100 * q^22 - 115 * q^23 - 120 * q^24 + 503 * q^25 - 132 * q^26 + 135 * q^27 + 140 * q^28 + 301 * q^29 - 36 * q^30 + 314 * q^31 - 160 * q^32 - 150 * q^33 + 396 * q^34 + 42 * q^35 + 180 * q^36 + 269 * q^37 - 240 * q^38 + 198 * q^39 - 48 * q^40 + 479 * q^41 - 210 * q^42 - 290 * q^43 - 200 * q^44 + 54 * q^45 + 230 * q^46 + 69 * q^47 + 240 * q^48 + 245 * q^49 - 1006 * q^50 - 594 * q^51 + 264 * q^52 + 339 * q^53 - 270 * q^54 + 957 * q^55 - 280 * q^56 + 360 * q^57 - 602 * q^58 + 2065 * q^59 + 72 * q^60 + 531 * q^61 - 628 * q^62 + 315 * q^63 + 320 * q^64 + 1227 * q^65 + 300 * q^66 + 855 * q^67 - 792 * q^68 - 345 * q^69 - 84 * q^70 - 863 * q^71 - 360 * q^72 + 618 * q^73 - 538 * q^74 + 1509 * q^75 + 480 * q^76 - 350 * q^77 - 396 * q^78 + 254 * q^79 + 96 * q^80 + 405 * q^81 - 958 * q^82 - 1700 * q^83 + 420 * q^84 + 1977 * q^85 + 580 * q^86 + 903 * q^87 + 400 * q^88 - 275 * q^89 - 108 * q^90 + 462 * q^91 - 460 * q^92 + 942 * q^93 - 138 * q^94 + 171 * q^95 - 480 * q^96 - 979 * q^97 - 490 * q^98 - 450 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	15.8741	1.41983	0.709913	−	0.704289i	$-0.248734\pi$
$5$	15.8741	1.41983	0.709913	+	0.704289i	$0.248734\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−31.7483	−1.00397
$11$	−10.2717	−0.281548	−0.140774	−	0.990042i	$-0.544959\pi$
$11$	−10.2717	−0.281548	−0.140774	+	0.990042i	$0.544959\pi$
$12$	12.0000	0.288675
$13$	−33.3338	−0.711164	−0.355582	−	0.934645i	$-0.615717\pi$
$13$	−33.3338	−0.711164	−0.355582	+	0.934645i	$0.615717\pi$
$14$	−14.0000	−0.267261
$15$	47.6224	0.819737
$16$	16.0000	0.250000
$17$	50.9562	0.726982	0.363491	−	0.931598i	$-0.381585\pi$
$17$	50.9562	0.726982	0.363491	+	0.931598i	$0.381585\pi$
$18$	−18.0000	−0.235702
$19$	−37.2079	−0.449268	−0.224634	−	0.974443i	$-0.572119\pi$
$19$	−37.2079	−0.449268	−0.224634	+	0.974443i	$0.572119\pi$
$20$	63.4966	0.709913
$21$	21.0000	0.218218
$22$	20.5434	0.199084
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	126.988	1.01591
$26$	66.6676	0.502869
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−46.6386	−0.298640	−0.149320	−	0.988789i	$-0.547708\pi$
$29$	−46.6386	−0.298640	−0.149320	+	0.988789i	$0.547708\pi$
$30$	−95.2448	−0.579642
$31$	53.8689	0.312101	0.156051	−	0.987749i	$-0.450124\pi$
$31$	53.8689	0.312101	0.156051	+	0.987749i	$0.450124\pi$
$32$	−32.0000	−0.176777
$33$	−30.8150	−0.162552
$34$	−101.912	−0.514054
$35$	111.119	0.536644
$36$	36.0000	0.166667
$37$	299.874	1.33240	0.666201	−	0.745772i	$-0.267919\pi$
$37$	299.874	1.33240	0.666201	+	0.745772i	$0.267919\pi$
$38$	74.4158	0.317680
$39$	−100.001	−0.410591
$40$	−126.993	−0.501984
$41$	496.665	1.89185	0.945927	−	0.324380i	$-0.105156\pi$
$41$	496.665	1.89185	0.945927	+	0.324380i	$0.105156\pi$
$42$	−42.0000	−0.154303
$43$	286.973	1.01774	0.508872	−	0.860842i	$-0.330063\pi$
$43$	286.973	1.01774	0.508872	+	0.860842i	$0.330063\pi$
$44$	−41.0867	−0.140774
$45$	142.867	0.473275
$46$	46.0000	0.147442
$47$	441.691	1.37079	0.685396	−	0.728170i	$-0.259629\pi$
$47$	441.691	1.37079	0.685396	+	0.728170i	$0.259629\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−253.977	−0.718354
$51$	152.869	0.419723
$52$	−133.335	−0.355582
$53$	404.159	1.04746	0.523731	−	0.851884i	$-0.324540\pi$
$53$	404.159	1.04746	0.523731	+	0.851884i	$0.324540\pi$
$54$	−54.0000	−0.136083
$55$	−163.054	−0.399749
$56$	−56.0000	−0.133631
$57$	−111.624	−0.259385
$58$	93.2771	0.211170
$59$	−3.89721	−0.00859955	−0.00429977	−	0.999991i	$-0.501369\pi$
$59$	−3.89721	−0.00859955	−0.00429977	+	0.999991i	$0.501369\pi$
$60$	190.490	0.409868
$61$	−758.345	−1.59174	−0.795870	−	0.605467i	$-0.792986\pi$
$61$	−758.345	−1.59174	−0.795870	+	0.605467i	$0.792986\pi$
$62$	−107.738	−0.220689
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−529.145	−1.00973
$66$	61.6301	0.114941
$67$	−461.880	−0.842204	−0.421102	−	0.907013i	$-0.638357\pi$
$67$	−461.880	−0.842204	−0.421102	+	0.907013i	$0.638357\pi$
$68$	203.825	0.363491
$69$	−69.0000	−0.120386
$70$	−222.238	−0.379464
$71$	−814.198	−1.36095	−0.680475	−	0.732771i	$-0.738227\pi$
$71$	−814.198	−1.36095	−0.680475	+	0.732771i	$0.738227\pi$
$72$	−72.0000	−0.117851
$73$	1176.38	1.88609	0.943045	−	0.332665i	$-0.107948\pi$
$73$	1176.38	1.88609	0.943045	+	0.332665i	$0.107948\pi$
$74$	−599.747	−0.942151
$75$	380.965	0.586534
$76$	−148.832	−0.224634
$77$	−71.9018	−0.106415
$78$	200.003	0.290331
$79$	949.684	1.35250	0.676252	−	0.736671i	$-0.263603\pi$
$79$	949.684	1.35250	0.676252	+	0.736671i	$0.263603\pi$
$80$	253.986	0.354957
$81$	81.0000	0.111111
$82$	−993.329	−1.33774
$83$	−141.363	−0.186948	−0.0934738	−	0.995622i	$-0.529797\pi$
$83$	−141.363	−0.186948	−0.0934738	+	0.995622i	$0.529797\pi$
$84$	84.0000	0.109109
$85$	808.886	1.03219
$86$	−573.946	−0.719653
$87$	−139.916	−0.172420
$88$	82.1734	0.0995422
$89$	−412.219	−0.490956	−0.245478	−	0.969402i	$-0.578945\pi$
$89$	−412.219	−0.490956	−0.245478	+	0.969402i	$0.578945\pi$
$90$	−285.734	−0.334656
$91$	−233.336	−0.268795
$92$	−92.0000	−0.104257
$93$	161.607	0.180192
$94$	−883.382	−0.969297
$95$	−590.644	−0.637882
$96$	−96.0000	−0.102062
$97$	−573.858	−0.600685	−0.300342	−	0.953831i	$-0.597101\pi$
$97$	−573.858	−0.600685	−0.300342	+	0.953831i	$0.597101\pi$
$98$	−98.0000	−0.101015
$99$	−92.4451	−0.0938493
$100$	507.953	0.507953
$101$	579.974	0.571382	0.285691	−	0.958322i	$-0.407777\pi$
$101$	579.974	0.571382	0.285691	+	0.958322i	$0.407777\pi$
$102$	−305.737	−0.296789
$103$	781.310	0.747425	0.373713	−	0.927545i	$-0.378085\pi$
$103$	781.310	0.747425	0.373713	+	0.927545i	$0.378085\pi$
$104$	266.670	0.251434
$105$	333.357	0.309831
$106$	−808.318	−0.740667
$107$	211.458	0.191051	0.0955255	−	0.995427i	$-0.469547\pi$
$107$	211.458	0.191051	0.0955255	+	0.995427i	$0.469547\pi$
$108$	108.000	0.0962250
$109$	1297.98	1.14058	0.570291	−	0.821443i	$-0.306830\pi$
$109$	1297.98	1.14058	0.570291	+	0.821443i	$0.306830\pi$
$110$	326.108	0.282665
$111$	899.621	0.769263
$112$	112.000	0.0944911
$113$	−2233.80	−1.85963	−0.929814	−	0.368030i	$-0.880032\pi$
$113$	−2233.80	−1.85963	−0.929814	+	0.368030i	$0.880032\pi$
$114$	223.248	0.183413
$115$	−365.105	−0.296054
$116$	−186.554	−0.149320
$117$	−300.004	−0.237055
$118$	7.79442	0.00608080
$119$	356.693	0.274773
$120$	−380.979	−0.289821
$121$	−1225.49	−0.920731
$122$	1516.69	1.12553
$123$	1489.99	1.09226
$124$	215.476	0.156051
$125$	31.5618	0.0225838
$126$	−126.000	−0.0890871
$127$	−1249.98	−0.873372	−0.436686	−	0.899614i	$-0.643848\pi$
$127$	−1249.98	−0.873372	−0.436686	+	0.899614i	$0.643848\pi$
$128$	−128.000	−0.0883883
$129$	860.919	0.587595
$130$	1058.29	0.713986
$131$	−2305.12	−1.53740	−0.768700	−	0.639610i	$-0.779096\pi$
$131$	−2305.12	−1.53740	−0.768700	+	0.639610i	$0.779096\pi$
$132$	−123.260	−0.0812759
$133$	−260.455	−0.169807
$134$	923.761	0.595528
$135$	428.602	0.273246
$136$	−407.650	−0.257027
$137$	1397.74	0.871658	0.435829	−	0.900029i	$-0.356455\pi$
$137$	1397.74	0.871658	0.435829	+	0.900029i	$0.356455\pi$
$138$	138.000	0.0851257
$139$	2348.74	1.43322	0.716611	−	0.697473i	$-0.245692\pi$
$139$	2348.74	1.43322	0.716611	+	0.697473i	$0.245692\pi$
$140$	444.476	0.268322
$141$	1325.07	0.791427
$142$	1628.40	0.962338
$143$	342.394	0.200227
$144$	144.000	0.0833333
$145$	−740.347	−0.424017
$146$	−2352.76	−1.33367
$147$	147.000	0.0824786
$148$	1199.49	0.666201
$149$	2917.80	1.60426	0.802131	−	0.597148i	$-0.203699\pi$
$149$	2917.80	1.60426	0.802131	+	0.597148i	$0.203699\pi$
$150$	−761.930	−0.414742
$151$	912.806	0.491941	0.245971	−	0.969277i	$-0.420893\pi$
$151$	912.806	0.491941	0.245971	+	0.969277i	$0.420893\pi$
$152$	297.663	0.158840
$153$	458.606	0.242327
$154$	143.804	0.0752469
$155$	855.123	0.443130
$156$	−400.005	−0.205295
$157$	1508.60	0.766876	0.383438	−	0.923567i	$-0.374740\pi$
$157$	1508.60	0.766876	0.383438	+	0.923567i	$0.374740\pi$
$158$	−1899.37	−0.956364
$159$	1212.48	0.604752
$160$	−507.972	−0.250992
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	158.139	0.0759901	0.0379951	−	0.999278i	$-0.487903\pi$
$163$	158.139	0.0759901	0.0379951	+	0.999278i	$0.487903\pi$
$164$	1986.66	0.945927
$165$	−489.162	−0.230795
$166$	282.727	0.132192
$167$	130.241	0.0603492	0.0301746	−	0.999545i	$-0.490394\pi$
$167$	130.241	0.0603492	0.0301746	+	0.999545i	$0.490394\pi$
$168$	−168.000	−0.0771517
$169$	−1085.86	−0.494246
$170$	−1617.77	−0.729867
$171$	−334.871	−0.149756
$172$	1147.89	0.508872
$173$	−2425.79	−1.06606	−0.533032	−	0.846095i	$-0.678947\pi$
$173$	−2425.79	−1.06606	−0.533032	+	0.846095i	$0.678947\pi$
$174$	279.831	0.121919
$175$	888.918	0.383976
$176$	−164.347	−0.0703870
$177$	−11.6916	−0.00496495
$178$	824.438	0.347158
$179$	122.123	0.0509939	0.0254970	−	0.999675i	$-0.491883\pi$
$179$	122.123	0.0509939	0.0254970	+	0.999675i	$0.491883\pi$
$180$	571.469	0.236638
$181$	479.445	0.196889	0.0984444	−	0.995143i	$-0.468613\pi$
$181$	479.445	0.196889	0.0984444	+	0.995143i	$0.468613\pi$
$182$	466.673	0.190067
$183$	−2275.04	−0.918992
$184$	184.000	0.0737210
$185$	4760.23	1.89178
$186$	−323.214	−0.127415
$187$	−523.406	−0.204680
$188$	1766.76	0.685396
$189$	189.000	0.0727393
$190$	1181.29	0.451051
$191$	−594.568	−0.225243	−0.112622	−	0.993638i	$-0.535925\pi$
$191$	−594.568	−0.225243	−0.112622	+	0.993638i	$0.535925\pi$
$192$	192.000	0.0721688
$193$	3016.98	1.12522	0.562609	−	0.826723i	$-0.309798\pi$
$193$	3016.98	1.12522	0.562609	+	0.826723i	$0.309798\pi$
$194$	1147.72	0.424748
$195$	−1587.44	−0.582967
$196$	196.000	0.0714286
$197$	−498.927	−0.180442	−0.0902209	−	0.995922i	$-0.528757\pi$
$197$	−498.927	−0.180442	−0.0902209	+	0.995922i	$0.528757\pi$
$198$	184.890	0.0663615
$199$	−2326.38	−0.828708	−0.414354	−	0.910116i	$-0.635992\pi$
$199$	−2326.38	−0.828708	−0.414354	+	0.910116i	$0.635992\pi$
$200$	−1015.91	−0.359177
$201$	−1385.64	−0.486247
$202$	−1159.95	−0.404028
$203$	−326.470	−0.112875
$204$	611.474	0.209862
$205$	7884.12	2.68610
$206$	−1562.62	−0.528509
$207$	−207.000	−0.0695048
$208$	−533.341	−0.177791
$209$	382.188	0.126490
$210$	−666.714	−0.219084
$211$	5228.94	1.70604	0.853022	−	0.521875i	$-0.174767\pi$
$211$	5228.94	1.70604	0.853022	+	0.521875i	$0.174767\pi$
$212$	1616.64	0.523731
$213$	−2442.59	−0.785745
$214$	−422.917	−0.135093
$215$	4555.45	1.44502
$216$	−216.000	−0.0680414
$217$	377.083	0.117963
$218$	−2595.95	−0.806514
$219$	3529.13	1.08893
$220$	−652.216	−0.199875
$221$	−1698.56	−0.517003
$222$	−1799.24	−0.543951
$223$	250.321	0.0751691	0.0375845	−	0.999293i	$-0.488034\pi$
$223$	250.321	0.0751691	0.0375845	+	0.999293i	$0.488034\pi$
$224$	−224.000	−0.0668153
$225$	1142.89	0.338635
$226$	4467.59	1.31496
$227$	−6030.20	−1.76316	−0.881582	−	0.472031i	$-0.843521\pi$
$227$	−6030.20	−1.76316	−0.881582	+	0.472031i	$0.843521\pi$
$228$	−446.495	−0.129692
$229$	4391.04	1.26711	0.633555	−	0.773698i	$-0.281595\pi$
$229$	4391.04	1.26711	0.633555	+	0.773698i	$0.281595\pi$
$230$	730.210	0.209342
$231$	−215.705	−0.0614388
$232$	373.108	0.105585
$233$	4621.89	1.29953	0.649764	−	0.760136i	$-0.274868\pi$
$233$	4621.89	1.29953	0.649764	+	0.760136i	$0.274868\pi$
$234$	600.008	0.167623
$235$	7011.46	1.94629
$236$	−15.5888	−0.00429977
$237$	2849.05	0.780868
$238$	−713.387	−0.194294
$239$	−6041.86	−1.63521	−0.817605	−	0.575779i	$-0.804699\pi$
$239$	−6041.86	−1.63521	−0.817605	+	0.575779i	$0.804699\pi$
$240$	761.959	0.204934
$241$	−481.586	−0.128721	−0.0643603	−	0.997927i	$-0.520501\pi$
$241$	−481.586	−0.128721	−0.0643603	+	0.997927i	$0.520501\pi$
$242$	2450.99	0.651055
$243$	243.000	0.0641500
$244$	−3033.38	−0.795870
$245$	777.833	0.202832
$246$	−2979.99	−0.772346
$247$	1240.28	0.319503
$248$	−430.951	−0.110345
$249$	−424.090	−0.107934
$250$	−63.1237	−0.0159692
$251$	661.776	0.166418	0.0832091	−	0.996532i	$-0.473483\pi$
$251$	661.776	0.166418	0.0832091	+	0.996532i	$0.473483\pi$
$252$	252.000	0.0629941
$253$	236.249	0.0587068
$254$	2499.97	0.617567
$255$	2426.66	0.595934
$256$	256.000	0.0625000
$257$	−5054.44	−1.22680	−0.613399	−	0.789773i	$-0.710198\pi$
$257$	−5054.44	−1.22680	−0.613399	+	0.789773i	$0.710198\pi$
$258$	−1721.84	−0.415492
$259$	2099.11	0.503601
$260$	−2116.58	−0.504864
$261$	−419.747	−0.0995467
$262$	4610.24	1.08711
$263$	−38.7966	−0.00909621	−0.00454810	−	0.999990i	$-0.501448\pi$
$263$	−38.7966	−0.00909621	−0.00454810	+	0.999990i	$0.501448\pi$
$264$	246.520	0.0574707
$265$	6415.67	1.48721
$266$	520.911	0.120072
$267$	−1236.66	−0.283454
$268$	−1847.52	−0.421102
$269$	−3973.89	−0.900716	−0.450358	−	0.892848i	$-0.648704\pi$
$269$	−3973.89	−0.900716	−0.450358	+	0.892848i	$0.648704\pi$
$270$	−857.203	−0.193214
$271$	−3702.84	−0.830006	−0.415003	−	0.909820i	$-0.636219\pi$
$271$	−3702.84	−0.830006	−0.415003	+	0.909820i	$0.636219\pi$
$272$	815.299	0.181745
$273$	−700.009	−0.155189
$274$	−2795.48	−0.616356
$275$	−1304.38	−0.286026
$276$	−276.000	−0.0601929
$277$	−3860.77	−0.837441	−0.418721	−	0.908115i	$-0.637521\pi$
$277$	−3860.77	−0.837441	−0.418721	+	0.908115i	$0.637521\pi$
$278$	−4697.49	−1.01344
$279$	484.820	0.104034
$280$	−888.952	−0.189732
$281$	7925.63	1.68258	0.841288	−	0.540588i	$-0.181798\pi$
$281$	7925.63	1.68258	0.841288	+	0.540588i	$0.181798\pi$
$282$	−2650.15	−0.559624
$283$	2387.81	0.501558	0.250779	−	0.968044i	$-0.419313\pi$
$283$	2387.81	0.501558	0.250779	+	0.968044i	$0.419313\pi$
$284$	−3256.79	−0.680475
$285$	−1771.93	−0.368281
$286$	−684.788	−0.141582
$287$	3476.65	0.715053
$288$	−288.000	−0.0589256
$289$	−2316.47	−0.471497
$290$	1480.69	0.299825
$291$	−1721.57	−0.346806
$292$	4705.51	0.943045
$293$	3479.11	0.693692	0.346846	−	0.937922i	$-0.387253\pi$
$293$	3479.11	0.693692	0.346846	+	0.937922i	$0.387253\pi$
$294$	−294.000	−0.0583212
$295$	−61.8648	−0.0122099
$296$	−2398.99	−0.471076
$297$	−277.335	−0.0541839
$298$	−5835.59	−1.13439
$299$	766.677	0.148288
$300$	1523.86	0.293267
$301$	2008.81	0.384671
$302$	−1825.61	−0.347855
$303$	1739.92	0.329888
$304$	−595.327	−0.112317
$305$	−12038.1	−2.26000
$306$	−917.212	−0.171351
$307$	317.498	0.0590247	0.0295124	−	0.999564i	$-0.490605\pi$
$307$	317.498	0.0590247	0.0295124	+	0.999564i	$0.490605\pi$
$308$	−287.607	−0.0532076
$309$	2343.93	0.431526
$310$	−1710.25	−0.313340
$311$	−8566.32	−1.56190	−0.780951	−	0.624592i	$-0.785265\pi$
$311$	−8566.32	−1.56190	−0.780951	+	0.624592i	$0.785265\pi$
$312$	800.011	0.145166
$313$	−2674.08	−0.482901	−0.241451	−	0.970413i	$-0.577623\pi$
$313$	−2674.08	−0.482901	−0.241451	+	0.970413i	$0.577623\pi$
$314$	−3017.20	−0.542263
$315$	1000.07	0.178881
$316$	3798.74	0.676252
$317$	7168.33	1.27007	0.635037	−	0.772481i	$-0.280985\pi$
$317$	7168.33	1.27007	0.635037	+	0.772481i	$0.280985\pi$
$318$	−2424.95	−0.427625
$319$	479.056	0.0840815
$320$	1015.94	0.177478
$321$	634.375	0.110303
$322$	322.000	0.0557278
$323$	−1895.97	−0.326609
$324$	324.000	0.0555556
$325$	−4233.00	−0.722476
$326$	−316.278	−0.0537331
$327$	3893.93	0.658516
$328$	−3973.32	−0.668871
$329$	3091.84	0.518111
$330$	978.324	0.163197
$331$	8797.18	1.46084	0.730418	−	0.683001i	$-0.239325\pi$
$331$	8797.18	1.46084	0.730418	+	0.683001i	$0.239325\pi$
$332$	−565.454	−0.0934738
$333$	2698.86	0.444134
$334$	−260.481	−0.0426733
$335$	−7331.95	−1.19578
$336$	336.000	0.0545545
$337$	8069.77	1.30442	0.652208	−	0.758040i	$-0.273843\pi$
$337$	8069.77	1.30442	0.652208	+	0.758040i	$0.273843\pi$
$338$	2171.72	0.349485
$339$	−6701.39	−1.07366
$340$	3235.54	0.516094
$341$	−553.324	−0.0878715
$342$	669.743	0.105893
$343$	343.000	0.0539949
$344$	−2295.78	−0.359827
$345$	−1095.32	−0.170927
$346$	4851.57	0.753821
$347$	−7363.64	−1.13920	−0.569598	−	0.821924i	$-0.692901\pi$
$347$	−7363.64	−1.13920	−0.569598	+	0.821924i	$0.692901\pi$
$348$	−559.663	−0.0862100
$349$	−3790.74	−0.581415	−0.290708	−	0.956812i	$-0.593891\pi$
$349$	−3790.74	−0.581415	−0.290708	+	0.956812i	$0.593891\pi$
$350$	−1777.84	−0.271512
$351$	−900.012	−0.136864
$352$	328.694	0.0497711
$353$	−6323.40	−0.953430	−0.476715	−	0.879058i	$-0.658173\pi$
$353$	−6323.40	−0.953430	−0.476715	+	0.879058i	$0.658173\pi$
$354$	23.3833	0.00351075
$355$	−12924.7	−1.93231
$356$	−1648.88	−0.245478
$357$	1070.08	0.158640
$358$	−244.246	−0.0360582
$359$	−13057.7	−1.91966	−0.959829	−	0.280585i	$-0.909471\pi$
$359$	−13057.7	−1.91966	−0.959829	+	0.280585i	$0.909471\pi$
$360$	−1142.94	−0.167328
$361$	−5474.57	−0.798159
$362$	−958.890	−0.139221
$363$	−3676.48	−0.531584
$364$	−933.346	−0.134397
$365$	18674.0	2.67792
$366$	4550.07	0.649825
$367$	5494.19	0.781456	0.390728	−	0.920506i	$-0.372223\pi$
$367$	5494.19	0.781456	0.390728	+	0.920506i	$0.372223\pi$
$368$	−368.000	−0.0521286
$369$	4469.98	0.630618
$370$	−9520.47	−1.33769
$371$	2829.11	0.395903
$372$	646.427	0.0900959
$373$	2068.31	0.287112	0.143556	−	0.989642i	$-0.454146\pi$
$373$	2068.31	0.287112	0.143556	+	0.989642i	$0.454146\pi$
$374$	1046.81	0.144731
$375$	94.6855	0.0130388
$376$	−3533.53	−0.484648
$377$	1554.64	0.212382
$378$	−378.000	−0.0514344
$379$	11476.5	1.55543	0.777714	−	0.628619i	$-0.216379\pi$
$379$	11476.5	1.55543	0.777714	+	0.628619i	$0.216379\pi$
$380$	−2362.57	−0.318941
$381$	−3749.95	−0.504241
$382$	1189.14	0.159271
$383$	−13726.7	−1.83133	−0.915667	−	0.401938i	$-0.868337\pi$
$383$	−13726.7	−1.83133	−0.915667	+	0.401938i	$0.868337\pi$
$384$	−384.000	−0.0510310
$385$	−1141.38	−0.151091
$386$	−6033.96	−0.795649
$387$	2582.76	0.339248
$388$	−2295.43	−0.300342
$389$	−12853.0	−1.67525	−0.837627	−	0.546242i	$-0.816058\pi$
$389$	−12853.0	−1.67525	−0.837627	+	0.546242i	$0.816058\pi$
$390$	3174.87	0.412220
$391$	−1171.99	−0.151586
$392$	−392.000	−0.0505076
$393$	−6915.36	−0.887618
$394$	997.853	0.127592
$395$	15075.4	1.92032
$396$	−369.780	−0.0469247
$397$	−2700.75	−0.341427	−0.170714	−	0.985321i	$-0.554607\pi$
$397$	−2700.75	−0.341427	−0.170714	+	0.985321i	$0.554607\pi$
$398$	4652.76	0.585985
$399$	−781.366	−0.0980382
$400$	2031.81	0.253977
$401$	−6659.56	−0.829333	−0.414667	−	0.909973i	$-0.636102\pi$
$401$	−6659.56	−0.829333	−0.414667	+	0.909973i	$0.636102\pi$
$402$	2771.28	0.343828
$403$	−1795.66	−0.221955
$404$	2319.90	0.285691
$405$	1285.81	0.157758
$406$	652.940	0.0798149
$407$	−3080.20	−0.375135
$408$	−1222.95	−0.148395
$409$	−954.476	−0.115393	−0.0576966	−	0.998334i	$-0.518376\pi$
$409$	−954.476	−0.115393	−0.0576966	+	0.998334i	$0.518376\pi$
$410$	−15768.2	−1.89936
$411$	4193.23	0.503252
$412$	3125.24	0.373713
$413$	−27.2805	−0.00325032
$414$	414.000	0.0491473
$415$	−2244.02	−0.265433
$416$	1066.68	0.125717
$417$	7046.23	0.827471
$418$	−764.376	−0.0894422
$419$	−8625.85	−1.00573	−0.502864	−	0.864365i	$-0.667721\pi$
$419$	−8625.85	−1.00573	−0.502864	+	0.864365i	$0.667721\pi$
$420$	1333.43	0.154916
$421$	1512.31	0.175073	0.0875364	−	0.996161i	$-0.472101\pi$
$421$	1512.31	0.175073	0.0875364	+	0.996161i	$0.472101\pi$
$422$	−10457.9	−1.20636
$423$	3975.22	0.456931
$424$	−3233.27	−0.370334
$425$	6470.84	0.738545
$426$	4885.19	0.555606
$427$	−5308.42	−0.601621
$428$	845.833	0.0955255
$429$	1027.18	0.115601
$430$	−9110.90	−1.02178
$431$	−5299.52	−0.592271	−0.296136	−	0.955146i	$-0.595698\pi$
$431$	−5299.52	−0.592271	−0.296136	+	0.955146i	$0.595698\pi$
$432$	432.000	0.0481125
$433$	−4831.89	−0.536272	−0.268136	−	0.963381i	$-0.586408\pi$
$433$	−4831.89	−0.536272	−0.268136	+	0.963381i	$0.586408\pi$
$434$	−754.165	−0.0834126
$435$	−2221.04	−0.244806
$436$	5191.90	0.570291
$437$	855.782	0.0936788
$438$	−7058.27	−0.769993
$439$	8915.20	0.969247	0.484623	−	0.874723i	$-0.338957\pi$
$439$	8915.20	0.969247	0.484623	+	0.874723i	$0.338957\pi$
$440$	1304.43	0.141333
$441$	441.000	0.0476190
$442$	3397.13	0.365576
$443$	15405.0	1.65218	0.826089	−	0.563540i	$-0.190561\pi$
$443$	15405.0	1.65218	0.826089	+	0.563540i	$0.190561\pi$
$444$	3598.48	0.384632
$445$	−6543.62	−0.697072
$446$	−500.641	−0.0531526
$447$	8753.39	0.926221
$448$	448.000	0.0472456
$449$	652.560	0.0685885	0.0342942	−	0.999412i	$-0.489082\pi$
$449$	652.560	0.0685885	0.0342942	+	0.999412i	$0.489082\pi$
$450$	−2285.79	−0.239451
$451$	−5101.58	−0.532648
$452$	−8935.19	−0.929814
$453$	2738.42	0.284022
$454$	12060.4	1.24675
$455$	−3704.02	−0.381642
$456$	892.990	0.0917063
$457$	−8597.71	−0.880052	−0.440026	−	0.897985i	$-0.645031\pi$
$457$	−8597.71	−0.880052	−0.440026	+	0.897985i	$0.645031\pi$
$458$	−8782.09	−0.895982
$459$	1375.82	0.139908
$460$	−1460.42	−0.148027
$461$	7978.04	0.806018	0.403009	−	0.915196i	$-0.367964\pi$
$461$	7978.04	0.806018	0.403009	+	0.915196i	$0.367964\pi$
$462$	431.411	0.0434438
$463$	−5894.05	−0.591619	−0.295810	−	0.955247i	$-0.595589\pi$
$463$	−5894.05	−0.591619	−0.295810	+	0.955247i	$0.595589\pi$
$464$	−746.217	−0.0746600
$465$	2565.37	0.255841
$466$	−9243.78	−0.918905
$467$	−10200.8	−1.01078	−0.505392	−	0.862890i	$-0.668652\pi$
$467$	−10200.8	−1.01078	−0.505392	+	0.862890i	$0.668652\pi$
$468$	−1200.02	−0.118527
$469$	−3233.16	−0.318323
$470$	−14022.9	−1.37623
$471$	4525.80	0.442756
$472$	31.1777	0.00304040
$473$	−2947.69	−0.286544
$474$	−5698.10	−0.552157
$475$	−4724.97	−0.456414
$476$	1426.77	0.137387
$477$	3637.43	0.349154
$478$	12083.7	1.15627
$479$	4699.97	0.448324	0.224162	−	0.974552i	$-0.428036\pi$
$479$	4699.97	0.448324	0.224162	+	0.974552i	$0.428036\pi$
$480$	−1523.92	−0.144910
$481$	−9995.92	−0.947557
$482$	963.172	0.0910193
$483$	−483.000	−0.0455016
$484$	−4901.97	−0.460365
$485$	−9109.50	−0.852868
$486$	−486.000	−0.0453609
$487$	−9696.36	−0.902225	−0.451113	−	0.892467i	$-0.648973\pi$
$487$	−9696.36	−0.902225	−0.451113	+	0.892467i	$0.648973\pi$
$488$	6066.76	0.562765
$489$	474.417	0.0438729
$490$	−1555.67	−0.143424
$491$	−4844.48	−0.445271	−0.222636	−	0.974902i	$-0.571466\pi$
$491$	−4844.48	−0.445271	−0.222636	+	0.974902i	$0.571466\pi$
$492$	5959.98	0.546131
$493$	−2376.52	−0.217106
$494$	−2480.56	−0.225923
$495$	−1467.49	−0.133250
$496$	861.903	0.0780254
$497$	−5699.39	−0.514391
$498$	848.180	0.0763210
$499$	−3059.15	−0.274442	−0.137221	−	0.990540i	$-0.543817\pi$
$499$	−3059.15	−0.274442	−0.137221	+	0.990540i	$0.543817\pi$
$500$	126.247	0.0112919
$501$	390.722	0.0348426
$502$	−1323.55	−0.117675
$503$	8840.38	0.783644	0.391822	−	0.920041i	$-0.371845\pi$
$503$	8840.38	0.783644	0.391822	+	0.920041i	$0.371845\pi$
$504$	−504.000	−0.0445435
$505$	9206.59	0.811263
$506$	−472.497	−0.0415120
$507$	−3257.58	−0.285353
$508$	−4999.94	−0.436686
$509$	12442.7	1.08352	0.541759	−	0.840534i	$-0.317758\pi$
$509$	12442.7	1.08352	0.541759	+	0.840534i	$0.317758\pi$
$510$	−4853.31	−0.421389
$511$	8234.64	0.712875
$512$	−512.000	−0.0441942
$513$	−1004.61	−0.0864616
$514$	10108.9	0.867477
$515$	12402.6	1.06121
$516$	3443.68	0.293797
$517$	−4536.91	−0.385944
$518$	−4198.23	−0.356100
$519$	−7277.36	−0.615492
$520$	4233.16	0.356993
$521$	−11868.4	−0.998014	−0.499007	−	0.866598i	$-0.666302\pi$
$521$	−11868.4	−0.998014	−0.499007	+	0.866598i	$0.666302\pi$
$522$	839.494	0.0703901
$523$	−8634.26	−0.721893	−0.360946	−	0.932587i	$-0.617546\pi$
$523$	−8634.26	−0.721893	−0.360946	+	0.932587i	$0.617546\pi$
$524$	−9220.48	−0.768700
$525$	2666.75	0.221689
$526$	77.5932	0.00643199
$527$	2744.96	0.226892
$528$	−493.041	−0.0406379
$529$	529.000	0.0434783
$530$	−12831.3	−1.05162
$531$	−35.0749	−0.00286652
$532$	−1041.82	−0.0849036
$533$	−16555.7	−1.34542
$534$	2473.31	0.200432
$535$	3356.72	0.271259
$536$	3695.04	0.297764
$537$	366.369	0.0294414
$538$	7947.79	0.636902
$539$	−503.312	−0.0402211
$540$	1714.41	0.136623
$541$	−20184.7	−1.60408	−0.802042	−	0.597268i	$-0.796253\pi$
$541$	−20184.7	−1.60408	−0.802042	+	0.597268i	$0.796253\pi$
$542$	7405.68	0.586903
$543$	1438.34	0.113674
$544$	−1630.60	−0.128513
$545$	20604.2	1.61943
$546$	1400.02	0.109735
$547$	319.314	0.0249595	0.0124798	−	0.999922i	$-0.496027\pi$
$547$	319.314	0.0249595	0.0124798	+	0.999922i	$0.496027\pi$
$548$	5590.97	0.435829
$549$	−6825.11	−0.530580
$550$	2608.77	0.202251
$551$	1735.32	0.134169
$552$	552.000	0.0425628
$553$	6647.79	0.511198
$554$	7721.54	0.592160
$555$	14280.7	1.09222
$556$	9394.97	0.716611
$557$	−7766.59	−0.590809	−0.295405	−	0.955372i	$-0.595454\pi$
$557$	−7766.59	−0.590809	−0.295405	+	0.955372i	$0.595454\pi$
$558$	−969.641	−0.0735630
$559$	−9565.90	−0.723782
$560$	1777.90	0.134161
$561$	−1570.22	−0.118172
$562$	−15851.3	−1.18976
$563$	1630.55	0.122059	0.0610297	−	0.998136i	$-0.480562\pi$
$563$	1630.55	0.122059	0.0610297	+	0.998136i	$0.480562\pi$
$564$	5300.29	0.395714
$565$	−35459.6	−2.64035
$566$	−4775.63	−0.354655
$567$	567.000	0.0419961
$568$	6513.58	0.481169
$569$	20220.5	1.48979	0.744894	−	0.667183i	$-0.232500\pi$
$569$	20220.5	1.48979	0.744894	+	0.667183i	$0.232500\pi$
$570$	3543.86	0.260414
$571$	4549.58	0.333439	0.166720	−	0.986004i	$-0.446683\pi$
$571$	4549.58	0.333439	0.166720	+	0.986004i	$0.446683\pi$
$572$	1369.58	0.100113
$573$	−1783.70	−0.130044
$574$	−6953.31	−0.505619
$575$	−2920.73	−0.211831
$576$	576.000	0.0416667
$577$	−20844.0	−1.50389	−0.751945	−	0.659225i	$-0.770884\pi$
$577$	−20844.0	−1.50389	−0.751945	+	0.659225i	$0.770884\pi$
$578$	4632.93	0.333399
$579$	9050.94	0.649645
$580$	−2961.39	−0.212009
$581$	−989.544	−0.0706595
$582$	3443.15	0.245229
$583$	−4151.39	−0.294911
$584$	−9411.02	−0.666834
$585$	−4762.31	−0.336576
$586$	−6958.22	−0.490514
$587$	10813.2	0.760319	0.380160	−	0.924921i	$-0.375869\pi$
$587$	10813.2	0.760319	0.380160	+	0.924921i	$0.375869\pi$
$588$	588.000	0.0412393
$589$	−2004.35	−0.140217
$590$	123.730	0.00863368
$591$	−1496.78	−0.104178
$592$	4797.98	0.333101
$593$	1079.81	0.0747763	0.0373881	−	0.999301i	$-0.488096\pi$
$593$	1079.81	0.0747763	0.0373881	+	0.999301i	$0.488096\pi$
$594$	554.671	0.0383138
$595$	5662.20	0.390130
$596$	11671.2	0.802131
$597$	−6979.14	−0.478455
$598$	−1533.35	−0.104855
$599$	−15261.4	−1.04101	−0.520504	−	0.853859i	$-0.674256\pi$
$599$	−15261.4	−1.04101	−0.520504	+	0.853859i	$0.674256\pi$
$600$	−3047.72	−0.207371
$601$	−955.575	−0.0648564	−0.0324282	−	0.999474i	$-0.510324\pi$
$601$	−955.575	−0.0648564	−0.0324282	+	0.999474i	$0.510324\pi$
$602$	−4017.62	−0.272003
$603$	−4156.92	−0.280735
$604$	3651.22	0.245971
$605$	−19453.6	−1.30728
$606$	−3479.85	−0.233266
$607$	4348.98	0.290806	0.145403	−	0.989372i	$-0.453552\pi$
$607$	4348.98	0.290806	0.145403	+	0.989372i	$0.453552\pi$
$608$	1190.65	0.0794200
$609$	−979.410	−0.0651686
$610$	24076.2	1.59806
$611$	−14723.2	−0.974858
$612$	1834.42	0.121164
$613$	−2862.63	−0.188614	−0.0943071	−	0.995543i	$-0.530064\pi$
$613$	−2862.63	−0.188614	−0.0943071	+	0.995543i	$0.530064\pi$
$614$	−634.997	−0.0417368
$615$	23652.4	1.55082
$616$	575.214	0.0376234
$617$	−686.482	−0.0447921	−0.0223961	−	0.999749i	$-0.507129\pi$
$617$	−686.482	−0.0447921	−0.0223961	+	0.999749i	$0.507129\pi$
$618$	−4687.86	−0.305135
$619$	−10300.1	−0.668812	−0.334406	−	0.942429i	$-0.608536\pi$
$619$	−10300.1	−0.668812	−0.334406	+	0.942429i	$0.608536\pi$
$620$	3420.49	0.221565
$621$	−621.000	−0.0401286
$622$	17132.6	1.10443
$623$	−2885.53	−0.185564
$624$	−1600.02	−0.102648
$625$	−15372.5	−0.983841
$626$	5348.17	0.341463
$627$	1146.56	0.0730292
$628$	6034.41	0.383438
$629$	15280.4	0.968633
$630$	−2000.14	−0.126488
$631$	15324.7	0.966825	0.483413	−	0.875393i	$-0.339397\pi$
$631$	15324.7	0.966825	0.483413	+	0.875393i	$0.339397\pi$
$632$	−7597.47	−0.478182
$633$	15686.8	0.984985
$634$	−14336.7	−0.898079
$635$	−19842.4	−1.24004
$636$	4849.91	0.302376
$637$	−1633.36	−0.101595
$638$	−958.113	−0.0594546
$639$	−7327.78	−0.453650
$640$	−2031.89	−0.125496
$641$	24345.3	1.50013	0.750063	−	0.661366i	$-0.230023\pi$
$641$	24345.3	1.50013	0.750063	+	0.661366i	$0.230023\pi$
$642$	−1268.75	−0.0779962
$643$	−19379.0	−1.18854	−0.594270	−	0.804265i	$-0.702559\pi$
$643$	−19379.0	−1.18854	−0.594270	+	0.804265i	$0.702559\pi$
$644$	−644.000	−0.0394055
$645$	13666.3	0.834282
$646$	3791.95	0.230948
$647$	−6853.96	−0.416471	−0.208236	−	0.978079i	$-0.566772\pi$
$647$	−6853.96	−0.416471	−0.208236	+	0.978079i	$0.566772\pi$
$648$	−648.000	−0.0392837
$649$	40.0309	0.00242119
$650$	8466.00	0.510867
$651$	1131.25	0.0681061
$652$	632.555	0.0379951
$653$	1110.32	0.0665394	0.0332697	−	0.999446i	$-0.489408\pi$
$653$	1110.32	0.0665394	0.0332697	+	0.999446i	$0.489408\pi$
$654$	−7787.85	−0.465641
$655$	−36591.8	−2.18284
$656$	7946.63	0.472963
$657$	10587.4	0.628697
$658$	−6183.67	−0.366360
$659$	12715.2	0.751612	0.375806	−	0.926698i	$-0.377366\pi$
$659$	12715.2	0.751612	0.375806	+	0.926698i	$0.377366\pi$
$660$	−1956.65	−0.115398
$661$	23984.3	1.41132	0.705659	−	0.708552i	$-0.250651\pi$
$661$	23984.3	1.41132	0.705659	+	0.708552i	$0.250651\pi$
$662$	−17594.4	−1.03297
$663$	−5095.69	−0.298492
$664$	1130.91	0.0660960
$665$	−4134.51	−0.241097
$666$	−5397.72	−0.314050
$667$	1072.69	0.0622708
$668$	520.962	0.0301746
$669$	750.962	0.0433989
$670$	14663.9	0.845546
$671$	7789.48	0.448151
$672$	−672.000	−0.0385758
$673$	15637.9	0.895684	0.447842	−	0.894113i	$-0.352193\pi$
$673$	15637.9	0.895684	0.447842	+	0.894113i	$0.352193\pi$
$674$	−16139.5	−0.922362
$675$	3428.68	0.195511
$676$	−4343.44	−0.247123
$677$	18722.8	1.06289	0.531443	−	0.847094i	$-0.321650\pi$
$677$	18722.8	1.06289	0.531443	+	0.847094i	$0.321650\pi$
$678$	13402.8	0.759190
$679$	−4017.00	−0.227038
$680$	−6471.09	−0.364934
$681$	−18090.6	−1.01796
$682$	1106.65	0.0621346
$683$	−22049.0	−1.23526	−0.617628	−	0.786470i	$-0.711906\pi$
$683$	−22049.0	−1.23526	−0.617628	+	0.786470i	$0.711906\pi$
$684$	−1339.49	−0.0748779
$685$	22188.0	1.23760
$686$	−686.000	−0.0381802
$687$	13173.1	0.731566
$688$	4591.57	0.254436
$689$	−13472.1	−0.744917
$690$	2190.63	0.120864
$691$	6124.49	0.337173	0.168587	−	0.985687i	$-0.446080\pi$
$691$	6124.49	0.337173	0.168587	+	0.985687i	$0.446080\pi$
$692$	−9703.14	−0.533032
$693$	−647.116	−0.0354717
$694$	14727.3	0.805533
$695$	37284.3	2.03493
$696$	1119.33	0.0609597
$697$	25308.1	1.37534
$698$	7581.49	0.411123
$699$	13865.7	0.750283
$700$	3555.67	0.191988
$701$	3502.93	0.188736	0.0943680	−	0.995537i	$-0.469917\pi$
$701$	3502.93	0.188736	0.0943680	+	0.995537i	$0.469917\pi$
$702$	1800.02	0.0967771
$703$	−11157.7	−0.598605
$704$	−657.387	−0.0351935
$705$	21034.4	1.12369
$706$	12646.8	0.674177
$707$	4059.82	0.215962
$708$	−46.7665	−0.00248248
$709$	−18821.4	−0.996970	−0.498485	−	0.866898i	$-0.666110\pi$
$709$	−18821.4	−0.996970	−0.498485	+	0.866898i	$0.666110\pi$
$710$	25849.4	1.36635
$711$	8547.15	0.450834
$712$	3297.75	0.173579
$713$	−1238.99	−0.0650777
$714$	−2140.16	−0.112176
$715$	5435.21	0.284287
$716$	488.493	0.0254970
$717$	−18125.6	−0.944089
$718$	26115.3	1.35740
$719$	6128.29	0.317867	0.158934	−	0.987289i	$-0.449194\pi$
$719$	6128.29	0.317867	0.158934	+	0.987289i	$0.449194\pi$
$720$	2285.88	0.118319
$721$	5469.17	0.282500
$722$	10949.1	0.564383
$723$	−1444.76	−0.0743169
$724$	1917.78	0.0984444
$725$	−5922.55	−0.303390
$726$	7352.96	0.375887
$727$	14041.8	0.716343	0.358171	−	0.933656i	$-0.383400\pi$
$727$	14041.8	0.716343	0.358171	+	0.933656i	$0.383400\pi$
$728$	1866.69	0.0950333
$729$	729.000	0.0370370
$730$	−37348.0	−1.89358
$731$	14623.1	0.739881
$732$	−9100.15	−0.459496
$733$	12213.1	0.615417	0.307708	−	0.951481i	$-0.400438\pi$
$733$	12213.1	0.615417	0.307708	+	0.951481i	$0.400438\pi$
$734$	−10988.4	−0.552573
$735$	2333.50	0.117105
$736$	736.000	0.0368605
$737$	4744.29	0.237121
$738$	−8939.96	−0.445914
$739$	−6672.85	−0.332158	−0.166079	−	0.986112i	$-0.553111\pi$
$739$	−6672.85	−0.332158	−0.166079	+	0.986112i	$0.553111\pi$
$740$	19040.9	0.945890
$741$	3720.84	0.184465
$742$	−5658.22	−0.279946
$743$	−1423.01	−0.0702626	−0.0351313	−	0.999383i	$-0.511185\pi$
$743$	−1423.01	−0.0702626	−0.0351313	+	0.999383i	$0.511185\pi$
$744$	−1292.85	−0.0637074
$745$	46317.5	2.27777
$746$	−4136.61	−0.203019
$747$	−1272.27	−0.0623159
$748$	−2093.62	−0.102340
$749$	1480.21	0.0722105
$750$	−189.371	−0.00921981
$751$	4953.47	0.240685	0.120343	−	0.992732i	$-0.461601\pi$
$751$	4953.47	0.240685	0.120343	+	0.992732i	$0.461601\pi$
$752$	7067.06	0.342698
$753$	1985.33	0.0960815
$754$	−3109.28	−0.150177
$755$	14490.0	0.698471
$756$	756.000	0.0363696
$757$	12917.0	0.620178	0.310089	−	0.950708i	$-0.399641\pi$
$757$	12917.0	0.620178	0.310089	+	0.950708i	$0.399641\pi$
$758$	−22953.0	−1.09985
$759$	708.746	0.0338944
$760$	4725.15	0.225525
$761$	19325.8	0.920577	0.460289	−	0.887769i	$-0.347746\pi$
$761$	19325.8	0.920577	0.460289	+	0.887769i	$0.347746\pi$
$762$	7499.91	0.356553
$763$	9085.83	0.431100
$764$	−2378.27	−0.112622
$765$	7279.97	0.344063
$766$	27453.4	1.29495
$767$	129.909	0.00611569
$768$	768.000	0.0360844
$769$	18647.6	0.874449	0.437224	−	0.899352i	$-0.355962\pi$
$769$	18647.6	0.874449	0.437224	+	0.899352i	$0.355962\pi$
$770$	2282.76	0.106837
$771$	−15163.3	−0.708292
$772$	12067.9	0.562609
$773$	−10941.6	−0.509108	−0.254554	−	0.967059i	$-0.581929\pi$
$773$	−10941.6	−0.509108	−0.254554	+	0.967059i	$0.581929\pi$
$774$	−5165.51	−0.239884
$775$	6840.72	0.317066
$776$	4590.86	0.212374
$777$	6297.34	0.290754
$778$	25706.0	1.18458
$779$	−18479.9	−0.849948
$780$	−6349.74	−0.291484
$781$	8363.18	0.383173
$782$	2343.99	0.107188
$783$	−1259.24	−0.0574733
$784$	784.000	0.0357143
$785$	23947.7	1.08883
$786$	13830.7	0.627641
$787$	9519.02	0.431152	0.215576	−	0.976487i	$-0.430837\pi$
$787$	9519.02	0.431152	0.215576	+	0.976487i	$0.430837\pi$
$788$	−1995.71	−0.0902209
$789$	−116.390	−0.00525170
$790$	−30150.8	−1.35787
$791$	−15636.6	−0.702873
$792$	739.561	0.0331807
$793$	25278.5	1.13199
$794$	5401.50	0.241426
$795$	19247.0	0.858643
$796$	−9305.53	−0.414354
$797$	−21472.9	−0.954339	−0.477169	−	0.878811i	$-0.658337\pi$
$797$	−21472.9	−0.954339	−0.477169	+	0.878811i	$0.658337\pi$
$798$	1562.73	0.0693235
$799$	22506.9	0.996542
$800$	−4063.62	−0.179589
$801$	−3709.97	−0.163652
$802$	13319.1	0.586427
$803$	−12083.4	−0.531025
$804$	−5542.56	−0.243123
$805$	−2555.74	−0.111898
$806$	3591.31	0.156946
$807$	−11921.7	−0.520028
$808$	−4639.79	−0.202014
$809$	−28791.0	−1.25122	−0.625611	−	0.780135i	$-0.715150\pi$
$809$	−28791.0	−1.25122	−0.625611	+	0.780135i	$0.715150\pi$
$810$	−2571.61	−0.111552
$811$	−23819.5	−1.03134	−0.515668	−	0.856788i	$-0.672456\pi$
$811$	−23819.5	−1.03134	−0.515668	+	0.856788i	$0.672456\pi$
$812$	−1305.88	−0.0564377
$813$	−11108.5	−0.479204
$814$	6160.41	0.265261
$815$	2510.32	0.107893
$816$	2445.90	0.104931
$817$	−10677.7	−0.457239
$818$	1908.95	0.0815953
$819$	−2100.03	−0.0895982
$820$	31536.5	1.34305
$821$	42561.1	1.80925	0.904623	−	0.426213i	$-0.140153\pi$
$821$	42561.1	1.80925	0.904623	+	0.426213i	$0.140153\pi$
$822$	−8386.45	−0.355853
$823$	−24033.2	−1.01791	−0.508957	−	0.860792i	$-0.669969\pi$
$823$	−24033.2	−1.01791	−0.508957	+	0.860792i	$0.669969\pi$
$824$	−6250.48	−0.264255
$825$	−3913.15	−0.165137
$826$	54.5609	0.00229833
$827$	−26191.0	−1.10127	−0.550635	−	0.834746i	$-0.685614\pi$
$827$	−26191.0	−1.10127	−0.550635	+	0.834746i	$0.685614\pi$
$828$	−828.000	−0.0347524
$829$	7370.32	0.308784	0.154392	−	0.988010i	$-0.450658\pi$
$829$	7370.32	0.308784	0.154392	+	0.988010i	$0.450658\pi$
$830$	4488.04	0.187690
$831$	−11582.3	−0.483497
$832$	−2133.36	−0.0888955
$833$	2496.85	0.103855
$834$	−14092.5	−0.585110
$835$	2067.46	0.0856853
$836$	1528.75	0.0632452
$837$	1454.46	0.0600640
$838$	17251.7	0.711158
$839$	−7865.99	−0.323676	−0.161838	−	0.986817i	$-0.551742\pi$
$839$	−7865.99	−0.323676	−0.161838	+	0.986817i	$0.551742\pi$
$840$	−2666.86	−0.109542
$841$	−22213.8	−0.910814
$842$	−3024.63	−0.123795
$843$	23776.9	0.971435
$844$	20915.8	0.853022
$845$	−17237.1	−0.701744
$846$	−7950.44	−0.323099
$847$	−8578.45	−0.348004
$848$	6466.54	0.261865
$849$	7163.44	0.289574
$850$	−12941.7	−0.522230
$851$	−6897.09	−0.277825
$852$	−9770.37	−0.392873
$853$	−15050.5	−0.604127	−0.302064	−	0.953288i	$-0.597675\pi$
$853$	−15050.5	−0.604127	−0.302064	+	0.953288i	$0.597675\pi$
$854$	10616.8	0.425411
$855$	−5315.79	−0.212627
$856$	−1691.67	−0.0675467
$857$	21842.7	0.870635	0.435317	−	0.900277i	$-0.356636\pi$
$857$	21842.7	0.870635	0.435317	+	0.900277i	$0.356636\pi$
$858$	−2054.36	−0.0817422
$859$	−46131.4	−1.83235	−0.916173	−	0.400784i	$-0.868738\pi$
$859$	−46131.4	−1.83235	−0.916173	+	0.400784i	$0.868738\pi$
$860$	18221.8	0.722509
$861$	10430.0	0.412836
$862$	10599.0	0.418799
$863$	34059.3	1.34344	0.671722	−	0.740803i	$-0.265555\pi$
$863$	34059.3	1.34344	0.671722	+	0.740803i	$0.265555\pi$
$864$	−864.000	−0.0340207
$865$	−38507.2	−1.51363
$866$	9663.78	0.379202
$867$	−6949.40	−0.272219
$868$	1508.33	0.0589816
$869$	−9754.85	−0.380795
$870$	4442.08	0.173104
$871$	15396.2	0.598945
$872$	−10383.8	−0.403257
$873$	−5164.72	−0.200228
$874$	−1711.56	−0.0662409
$875$	220.933	0.00853588
$876$	14116.5	0.544467
$877$	2602.02	0.100187	0.0500935	−	0.998745i	$-0.484048\pi$
$877$	2602.02	0.100187	0.0500935	+	0.998745i	$0.484048\pi$
$878$	−17830.4	−0.685361
$879$	10437.3	0.400503
$880$	−2608.86	−0.0999373
$881$	24859.3	0.950658	0.475329	−	0.879808i	$-0.342329\pi$
$881$	24859.3	0.950658	0.475329	+	0.879808i	$0.342329\pi$
$882$	−882.000	−0.0336718
$883$	−10786.7	−0.411100	−0.205550	−	0.978647i	$-0.565898\pi$
$883$	−10786.7	−0.411100	−0.205550	+	0.978647i	$0.565898\pi$
$884$	−6794.25	−0.258502
$885$	−185.595	−0.00704937
$886$	−30810.0	−1.16827
$887$	−12952.4	−0.490302	−0.245151	−	0.969485i	$-0.578837\pi$
$887$	−12952.4	−0.490302	−0.245151	+	0.969485i	$0.578837\pi$
$888$	−7196.96	−0.271976
$889$	−8749.89	−0.330104
$890$	13087.2	0.492905
$891$	−832.006	−0.0312831
$892$	1001.28	0.0375845
$893$	−16434.4	−0.615853
$894$	−17506.8	−0.654938
$895$	1938.60	0.0724025
$896$	−896.000	−0.0334077
$897$	2300.03	0.0856141
$898$	−1305.12	−0.0484994
$899$	−2512.37	−0.0932060
$900$	4571.58	0.169318
$901$	20594.4	0.761486
$902$	10203.2	0.376639
$903$	6026.43	0.222090
$904$	17870.4	0.657478
$905$	7610.78	0.279548
$906$	−5476.84	−0.200834
$907$	−2600.94	−0.0952179	−0.0476090	−	0.998866i	$-0.515160\pi$
$907$	−2600.94	−0.0952179	−0.0476090	+	0.998866i	$0.515160\pi$
$908$	−24120.8	−0.881582
$909$	5219.77	0.190461
$910$	7408.03	0.269861
$911$	−11794.9	−0.428958	−0.214479	−	0.976729i	$-0.568805\pi$
$911$	−11794.9	−0.428958	−0.214479	+	0.976729i	$0.568805\pi$
$912$	−1785.98	−0.0648462
$913$	1452.04	0.0526347
$914$	17195.4	0.622291
$915$	−36114.2	−1.30481
$916$	17564.2	0.633555
$917$	−16135.8	−0.581082
$918$	−2751.63	−0.0989297
$919$	33386.9	1.19840	0.599201	−	0.800599i	$-0.295485\pi$
$919$	33386.9	1.19840	0.599201	+	0.800599i	$0.295485\pi$
$920$	2920.84	0.104671
$921$	952.495	0.0340779
$922$	−15956.1	−0.569941
$923$	27140.3	0.967859
$924$	−862.821	−0.0307194
$925$	38080.4	1.35360
$926$	11788.1	0.418338
$927$	7031.79	0.249142
$928$	1492.43	0.0527926
$929$	21498.0	0.759233	0.379617	−	0.925144i	$-0.376056\pi$
$929$	21498.0	0.759233	0.379617	+	0.925144i	$0.376056\pi$
$930$	−5130.74	−0.180907
$931$	−1823.19	−0.0641811
$932$	18487.6	0.649764
$933$	−25699.0	−0.901765
$934$	20401.6	0.714732
$935$	−8308.61	−0.290610
$936$	2400.03	0.0838115
$937$	2158.99	0.0752733	0.0376366	−	0.999291i	$-0.488017\pi$
$937$	2158.99	0.0752733	0.0376366	+	0.999291i	$0.488017\pi$
$938$	6466.32	0.225088
$939$	−8022.25	−0.278803
$940$	28045.9	0.973144
$941$	−12948.7	−0.448582	−0.224291	−	0.974522i	$-0.572007\pi$
$941$	−12948.7	−0.448582	−0.224291	+	0.974522i	$0.572007\pi$
$942$	−9051.61	−0.313076
$943$	−11423.3	−0.394479
$944$	−62.3553	−0.00214989
$945$	3000.21	0.103277
$946$	5895.39	0.202617
$947$	−41937.0	−1.43904	−0.719519	−	0.694473i	$-0.755638\pi$
$947$	−41937.0	−1.43904	−0.719519	+	0.694473i	$0.755638\pi$
$948$	11396.2	0.390434
$949$	−39213.1	−1.34132
$950$	9449.94	0.322733
$951$	21505.0	0.733278
$952$	−2853.55	−0.0971471
$953$	−451.100	−0.0153332	−0.00766660	−	0.999971i	$-0.502440\pi$
$953$	−451.100	−0.0153332	−0.00766660	+	0.999971i	$0.502440\pi$
$954$	−7274.86	−0.246889
$955$	−9438.26	−0.319806
$956$	−24167.4	−0.817605
$957$	1437.17	0.0485445
$958$	−9399.94	−0.317013
$959$	9784.20	0.329456
$960$	3047.83	0.102467
$961$	−26889.1	−0.902593
$962$	19991.8	0.670024
$963$	1903.13	0.0636836
$964$	−1926.34	−0.0643603
$965$	47892.0	1.59761
$966$	966.000	0.0321745
$967$	−36103.9	−1.20064	−0.600322	−	0.799758i	$-0.704961\pi$
$967$	−36103.9	−1.20064	−0.600322	+	0.799758i	$0.704961\pi$
$968$	9803.94	0.325527
$969$	−5687.92	−0.188568
$970$	18219.0	0.603069
$971$	17206.2	0.568663	0.284331	−	0.958726i	$-0.408228\pi$
$971$	17206.2	0.568663	0.284331	+	0.958726i	$0.408228\pi$
$972$	972.000	0.0320750
$973$	16441.2	0.541707
$974$	19392.7	0.637970
$975$	−12699.0	−0.417121
$976$	−12133.5	−0.397935
$977$	−12168.5	−0.398470	−0.199235	−	0.979952i	$-0.563846\pi$
$977$	−12168.5	−0.398470	−0.199235	+	0.979952i	$0.563846\pi$
$978$	−948.833	−0.0310228
$979$	4234.18	0.138228
$980$	3111.33	0.101416
$981$	11681.8	0.380194
$982$	9688.96	0.314854
$983$	−11437.6	−0.371110	−0.185555	−	0.982634i	$-0.559408\pi$
$983$	−11437.6	−0.371110	−0.185555	+	0.982634i	$0.559408\pi$
$984$	−11920.0	−0.386173
$985$	−7920.03	−0.256196
$986$	4753.05	0.153517
$987$	9275.51	0.299131
$988$	4961.12	0.159751
$989$	−6600.38	−0.212214
$990$	2934.97	0.0942218
$991$	−8278.58	−0.265366	−0.132683	−	0.991159i	$-0.542359\pi$
$991$	−8278.58	−0.265366	−0.132683	+	0.991159i	$0.542359\pi$
$992$	−1723.81	−0.0551723
$993$	26391.5	0.843414
$994$	11398.8	0.363729
$995$	−36929.3	−1.17662
$996$	−1696.36	−0.0539671
$997$	29335.3	0.931854	0.465927	−	0.884823i	$-0.345721\pi$
$997$	29335.3	0.931854	0.465927	+	0.884823i	$0.345721\pi$
$998$	6118.30	0.194060
$999$	8096.59	0.256421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.o.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.o.1.4	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.8741 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.8741 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -31.7483 q^{10} -10.2717 q^{11} +12.0000 q^{12} -33.3338 q^{13} -14.0000 q^{14} +47.6224 q^{15} +16.0000 q^{16} +50.9562 q^{17} -18.0000 q^{18} -37.2079 q^{19} +63.4966 q^{20} +21.0000 q^{21} +20.5434 q^{22} -23.0000 q^{23} -24.0000 q^{24} +126.988 q^{25} +66.6676 q^{26} +27.0000 q^{27} +28.0000 q^{28} -46.6386 q^{29} -95.2448 q^{30} +53.8689 q^{31} -32.0000 q^{32} -30.8150 q^{33} -101.912 q^{34} +111.119 q^{35} +36.0000 q^{36} +299.874 q^{37} +74.4158 q^{38} -100.001 q^{39} -126.993 q^{40} +496.665 q^{41} -42.0000 q^{42} +286.973 q^{43} -41.0867 q^{44} +142.867 q^{45} +46.0000 q^{46} +441.691 q^{47} +48.0000 q^{48} +49.0000 q^{49} -253.977 q^{50} +152.869 q^{51} -133.335 q^{52} +404.159 q^{53} -54.0000 q^{54} -163.054 q^{55} -56.0000 q^{56} -111.624 q^{57} +93.2771 q^{58} -3.89721 q^{59} +190.490 q^{60} -758.345 q^{61} -107.738 q^{62} +63.0000 q^{63} +64.0000 q^{64} -529.145 q^{65} +61.6301 q^{66} -461.880 q^{67} +203.825 q^{68} -69.0000 q^{69} -222.238 q^{70} -814.198 q^{71} -72.0000 q^{72} +1176.38 q^{73} -599.747 q^{74} +380.965 q^{75} -148.832 q^{76} -71.9018 q^{77} +200.003 q^{78} +949.684 q^{79} +253.986 q^{80} +81.0000 q^{81} -993.329 q^{82} -141.363 q^{83} +84.0000 q^{84} +808.886 q^{85} -573.946 q^{86} -139.916 q^{87} +82.1734 q^{88} -412.219 q^{89} -285.734 q^{90} -233.336 q^{91} -92.0000 q^{92} +161.607 q^{93} -883.382 q^{94} -590.644 q^{95} -96.0000 q^{96} -573.858 q^{97} -98.0000 q^{98} -92.4451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} + 6 q^{5} - 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} - 12 q^{10} - 50 q^{11} + 60 q^{12} + 66 q^{13} - 70 q^{14} + 18 q^{15} + 80 q^{16} - 198 q^{17} - 90 q^{18} + 120 q^{19} + 24 q^{20} + 105 q^{21} + 100 q^{22} - 115 q^{23} - 120 q^{24} + 503 q^{25} - 132 q^{26} + 135 q^{27} + 140 q^{28} + 301 q^{29} - 36 q^{30} + 314 q^{31} - 160 q^{32} - 150 q^{33} + 396 q^{34} + 42 q^{35} + 180 q^{36} + 269 q^{37} - 240 q^{38} + 198 q^{39} - 48 q^{40} + 479 q^{41} - 210 q^{42} - 290 q^{43} - 200 q^{44} + 54 q^{45} + 230 q^{46} + 69 q^{47} + 240 q^{48} + 245 q^{49} - 1006 q^{50} - 594 q^{51} + 264 q^{52} + 339 q^{53} - 270 q^{54} + 957 q^{55} - 280 q^{56} + 360 q^{57} - 602 q^{58} + 2065 q^{59} + 72 q^{60} + 531 q^{61} - 628 q^{62} + 315 q^{63} + 320 q^{64} + 1227 q^{65} + 300 q^{66} + 855 q^{67} - 792 q^{68} - 345 q^{69} - 84 q^{70} - 863 q^{71} - 360 q^{72} + 618 q^{73} - 538 q^{74} + 1509 q^{75} + 480 q^{76} - 350 q^{77} - 396 q^{78} + 254 q^{79} + 96 q^{80} + 405 q^{81} - 958 q^{82} - 1700 q^{83} + 420 q^{84} + 1977 q^{85} + 580 q^{86} + 903 q^{87} + 400 q^{88} - 275 q^{89} - 108 q^{90} + 462 q^{91} - 460 q^{92} + 942 q^{93} - 138 q^{94} + 171 q^{95} - 480 q^{96} - 979 q^{97} - 490 q^{98} - 450 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 + 6 * q^5 - 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 - 12 * q^10 - 50 * q^11 + 60 * q^12 + 66 * q^13 - 70 * q^14 + 18 * q^15 + 80 * q^16 - 198 * q^17 - 90 * q^18 + 120 * q^19 + 24 * q^20 + 105 * q^21 + 100 * q^22 - 115 * q^23 - 120 * q^24 + 503 * q^25 - 132 * q^26 + 135 * q^27 + 140 * q^28 + 301 * q^29 - 36 * q^30 + 314 * q^31 - 160 * q^32 - 150 * q^33 + 396 * q^34 + 42 * q^35 + 180 * q^36 + 269 * q^37 - 240 * q^38 + 198 * q^39 - 48 * q^40 + 479 * q^41 - 210 * q^42 - 290 * q^43 - 200 * q^44 + 54 * q^45 + 230 * q^46 + 69 * q^47 + 240 * q^48 + 245 * q^49 - 1006 * q^50 - 594 * q^51 + 264 * q^52 + 339 * q^53 - 270 * q^54 + 957 * q^55 - 280 * q^56 + 360 * q^57 - 602 * q^58 + 2065 * q^59 + 72 * q^60 + 531 * q^61 - 628 * q^62 + 315 * q^63 + 320 * q^64 + 1227 * q^65 + 300 * q^66 + 855 * q^67 - 792 * q^68 - 345 * q^69 - 84 * q^70 - 863 * q^71 - 360 * q^72 + 618 * q^73 - 538 * q^74 + 1509 * q^75 + 480 * q^76 - 350 * q^77 - 396 * q^78 + 254 * q^79 + 96 * q^80 + 405 * q^81 - 958 * q^82 - 1700 * q^83 + 420 * q^84 + 1977 * q^85 + 580 * q^86 + 903 * q^87 + 400 * q^88 - 275 * q^89 - 108 * q^90 + 462 * q^91 - 460 * q^92 + 942 * q^93 - 138 * q^94 + 171 * q^95 - 480 * q^96 - 979 * q^97 - 490 * q^98 - 450 * q^99

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